{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# PDE-FIND for the Quantum Harmonic Oscillator\n",
    "\n",
    "By Samuel Rudy, 2016\n",
    "\n",
    "This notebook demonstrates PDE-FIND on the schrodinger equation with a parabolic well potential.  \n",
    "$$\n",
    "iu_t = \\frac{-1}{2}u_{xx} + \\frac{x^2}{2}u\n",
    "$$\n",
    "We assume full knowledge of the complex wave function rather than just the squared magnitude and also know that there is a potenital function $\\frac{x^2}{2}$, but it is unknown if or how it appears in the PDE."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    }
   ],
   "source": [
    "%pylab inline\n",
    "pylab.rcParams['figure.figsize'] = (12, 8)\n",
    "import numpy as np \n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "from PDE_FIND import *\n",
    "import scipy.io as sio"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x7fd55bced350>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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HuiFv/qVSCYwxLURqNALdqC3DEKmeqyQRFPK6apUPS3SG7mkA8pinRbNzLs6Z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SJDTdPdywql5Vu9J+gN6jsbGxKU/593pcMQLL7QNV9hNSg3p5PJywAiYJAIAtvkpEgt32YOqq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\nAVIY0cKtXp+0AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fd55bd315d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Load data - solution to schrodinger in parabolic well\n",
    "data = sio.loadmat('./canonicalPDEs/harmonic_osc.mat')\n",
    "u = data['usol']\n",
    "x = data['x'][0]\n",
    "t = data['t'][:,0]\n",
    "dt = t[1] - t[0]\n",
    "dx = x[1] - x[0]\n",
    "n = len(x)\n",
    "m = len(t)\n",
    "potential = np.vstack([0.5*np.power(x,2).reshape((1,n)) for _ in range(m)])\n",
    "\n",
    "X, T = np.meshgrid(x, t)\n",
    "fig = figure()\n",
    "ax = fig.gca(projection='3d')\n",
    "surf = ax.plot_surface(X, T, abs(u), rstride=1, cstride=1, cmap=cm.coolwarm,\n",
    "    linewidth=0, antialiased=False)\n",
    "title(r'Quantum Harmonic Oscillator: $|\\psi|$', fontsize = 20)\n",
    "xlabel('x', fontsize = 16)\n",
    "ylabel('t', fontsize = 16)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "## Build Library of Candidate Terms\n",
    "\n",
    "We first differentiate the data along the spatial and temporal directions and construct a library of terms including nonlinearities and partial derivatives.  The matrix Theta is constructed so that each column is a potential term in the PDE, listed below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['',\n",
       " 'u_{x}',\n",
       " 'u_{xx}',\n",
       " 'u_{xxx}',\n",
       " '|u|V',\n",
       " 'V^2',\n",
       " '|u|^2',\n",
       " 'u',\n",
       " 'u|u|',\n",
       " 'V',\n",
       " 'uV',\n",
       " '|u|',\n",
       " 'u^2',\n",
       " '|u|Vu_{x}',\n",
       " 'V^2u_{x}',\n",
       " '|u|^2u_{x}',\n",
       " 'uu_{x}',\n",
       " 'u|u|u_{x}',\n",
       " 'Vu_{x}',\n",
       " 'uVu_{x}',\n",
       " '|u|u_{x}',\n",
       " 'u^2u_{x}',\n",
       " '|u|Vu_{xx}',\n",
       " 'V^2u_{xx}',\n",
       " '|u|^2u_{xx}',\n",
       " 'uu_{xx}',\n",
       " 'u|u|u_{xx}',\n",
       " 'Vu_{xx}',\n",
       " 'uVu_{xx}',\n",
       " '|u|u_{xx}',\n",
       " 'u^2u_{xx}',\n",
       " '|u|Vu_{xxx}',\n",
       " 'V^2u_{xxx}',\n",
       " '|u|^2u_{xxx}',\n",
       " 'uu_{xxx}',\n",
       " 'u|u|u_{xxx}',\n",
       " 'Vu_{xxx}',\n",
       " 'uVu_{xxx}',\n",
       " '|u|u_{xxx}',\n",
       " 'u^2u_{xxx}']"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ut = np.zeros((m,n), dtype=np.complex64)\n",
    "ux = np.zeros((m,n), dtype=np.complex64)\n",
    "uxx = np.zeros((m,n), dtype=np.complex64)\n",
    "uxxx = np.zeros((m,n), dtype=np.complex64)\n",
    "\n",
    "for i in range(n):\n",
    "    ut[:,i] = FiniteDiff(u[:,i], dt, 1)\n",
    "for i in range(m):\n",
    "    ux[i,:] = FiniteDiff(u[i,:], dx, 1)\n",
    "    uxx[i,:] = FiniteDiff(u[i,:], dx, 2)\n",
    "    uxxx[i,:] = FiniteDiff(u[i,:], dx, 3)\n",
    "    \n",
    "ut = np.reshape(ut, (n*m,1), order='F')\n",
    "ux = np.reshape(ux, (n*m,1), order='F')\n",
    "uxx = np.reshape(uxx, (n*m,1), order='F')\n",
    "uxxx = np.reshape(uxxx, (n*m,1), order='F')\n",
    "X_ders = np.hstack([np.ones((n*m,1)),ux,uxx,uxxx])\n",
    "X_data = np.hstack([np.reshape(u, (n*m,1), order='F'), \n",
    "                    np.reshape(abs(u), (n*m,1), order='F'), \n",
    "                    np.reshape(potential, (n*m,1), order='F')])\n",
    "derivatives_description = ['','u_{x}','u_{xx}', 'u_{xxx}']\n",
    "\n",
    "X, descr = build_Theta(X_data, X_ders, derivatives_description, 2, data_description = ['u','|u|','V'])\n",
    "descr"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Solve for PDE\n",
    "\n",
    "Now that the linear system is constructed we look for a sparse solution.  Below, the result has the correct sparsity pattern (the right terms in the PDE).  Though they should not have real components, a threshold after identifying the PDE would eliminate those."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "PDE derived using STRidge\n",
      "u_t = (0.000006 +0.498821i)u_{xx}\n",
      "    + (0.000012 -0.997386i)uV\n",
      "   \n"
     ]
    }
   ],
   "source": [
    "# Solve with STRidge\n",
    "w = TrainSTRidge(X,ut,10**-5,10)\n",
    "print \"PDE derived using STRidge\"\n",
    "print_pde(w, descr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Error using PDE-FIND to identify the Schrodinger equation:\n",
      "\n",
      "Mean parameter error: 0.2486029039 %\n",
      "Standard deviation of parameter error: 0.0127998504848 %\n"
     ]
    }
   ],
   "source": [
    "err = abs(np.array([(1j*(0.5-0.498821)+0.000006)*100/0.5, (1j*(1-0.997386)+0.000012)*100]))\n",
    "print \"Error using PDE-FIND to identify the Schrodinger equation:\\n\"\n",
    "print \"Mean parameter error:\", mean(err), '%'\n",
    "print \"Standard deviation of parameter error:\", std(err), '%'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Identifying the PDE with added noise\n",
    "\n",
    "Now we try to identify the same PDE but with artificially added noise.  We take 1 percent of the standard deviation of the solution and add in noise with that magnitude.  The noisy solution is then differentiated using polynomials rather than finite differences and passed into PDE-FIND.  We again find the correct PDE, in terms of sparsity, this time with slightly larger error."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "numpy.random.seed(0)\n",
    "un = u + 0.01/np.sqrt(2)*(std(real(u))*np.random.randn(m,n) + 1j*std(imag(u))*np.random.randn(m,n))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "width_x = 10\n",
    "width_t = 10\n",
    "deg = 6\n",
    "\n",
    "m2 = m-2*width_t\n",
    "n2 = n-2*width_x\n",
    "\n",
    "utn = np.zeros((m2,n2), dtype=np.complex64)\n",
    "uxn = np.zeros((m2,n2), dtype=np.complex64)\n",
    "uxxn = np.zeros((m2,n2), dtype=np.complex64)\n",
    "uxxxn = np.zeros((m2,n2), dtype=np.complex64)\n",
    "\n",
    "for i in range(n2):\n",
    "    utn[:,i] = PolyDiff(real(un[:,i+width_x]), dt*np.arange(m), deg = deg, width = width_t)[:,0]\n",
    "    utn[:,i] = utn[:,i]+1j*PolyDiff(imag(un[:,i+width_x]), dt*np.arange(m), deg = deg, width = width_t)[:,0]\n",
    "\n",
    "for i in range(m2):\n",
    "    x_derivatives = PolyDiff(real(un[i+width_t,:]), dx*np.arange(n), deg = deg, diff = 3, width = width_x)\n",
    "    x_derivatives = x_derivatives+1j*PolyDiff(imag(un[i+width_t,:]), dx*np.arange(n), deg = deg, diff = 3, width = width_x)\n",
    "    uxn[i,:] = x_derivatives[:,0]\n",
    "    uxxn[i,:] = x_derivatives[:,1]\n",
    "    uxxxn[i,:] = x_derivatives[:,2]\n",
    "\n",
    "utn = np.reshape(utn, (n2*m2,1), order='F')\n",
    "uxn = np.reshape(uxn, (n2*m2,1), order='F')\n",
    "uxxn = np.reshape(uxxn, (n2*m2,1), order='F')\n",
    "uxxxn = np.reshape(uxxxn, (n2*m2,1), order='F')\n",
    "Xn_ders = np.hstack([np.ones((n2*m2,1)),uxn,uxxn,uxxxn])\n",
    "Xn_data = np.hstack([np.reshape(un[width_t:m-width_t,width_x:n-width_x], (n2*m2,1), order='F'),\n",
    "                     np.reshape(abs(un[width_t:m-width_t,width_x:n-width_x]), (n2*m2,1), order='F'),\n",
    "                     np.reshape(potential[width_t:m-width_t,width_x:n-width_x], (n2*m2,1), order='F')])\n",
    "derivatives_description = ['','u_{x}','u_{xx}', 'u_{xxx}']\n",
    "\n",
    "Xn, _ = build_Theta(Xn_data, Xn_ders, derivatives_description, 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "PDE derived using STRidge\n",
      "u_t = (0.000087 +0.416703i)u_{xx}\n",
      "    + (-0.000475 -1.027185i)uV\n",
      "   \n"
     ]
    }
   ],
   "source": [
    "# Solve with STRidge\n",
    "lam = 10**-5\n",
    "d_tol = 10\n",
    "w = TrainSTRidge(Xn,utn,lam,d_tol)\n",
    "print \"PDE derived using STRidge\"\n",
    "print_pde(w, descr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Error using PDE-FIND to identify the Schrodinger equation with added noise:\n",
      "\n",
      "Mean parameter error: 0.251060883673 %\n",
      "Standard deviation of parameter error: 0.0146197704967 %\n"
     ]
    }
   ],
   "source": [
    "err = abs(np.array([(1j*(0.5-0.498821)+0.000087)*100/0.5, (1j*(1-0.997386)+0.000475)*100]))\n",
    "print \"Error using PDE-FIND to identify the Schrodinger equation with added noise:\\n\"\n",
    "print \"Mean parameter error:\", mean(err), '%'\n",
    "print \"Standard deviation of parameter error:\", std(err), '%'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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